WASHINGTON (CNN) -- The battle over the word "bitter" between Sens. Barack Obama and Hillary Clinton has sparked a new look at the candidates and their stance on the Second Amendment.

At a closed-door fundraiser just over a week ago, the Illinois senator referred to some small-town Pennsylvanians as "bitter" people who "cling to guns and religion."

"I didn't say it as well as I should have," Obama admitted in Muncie, Indiana, on Saturday, the day after he first defended his comments, "because the truth is that these traditions that are passed on from generation to generation -- those are important."

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"You know, my dad took me out behind the cottage that my grandfather built on a little lake called Lake Winola outside of Scranton and taught me how to shoot when I was a little girl," Clinton said in Valparaiso, Indiana, on Saturday.

"Some people now continue to teach their children and their grandchildren. It's part of culture. It's part of a way of life. People enjoy hunting and shooting because it's an important part of who they are. Not because they are bitter." Watch Clinton discuss guns »

A visibly agitated Obama accused Clinton on Sunday of acting like "Annie Oakley ... packin' a six-shooter" in her attempts to connect with gun owners.

"She's running around talking about how this is an insult to sportsmen, how she values the Second Amendment," he said, his voice rising. "She's talking like she's Annie Oakley! Hillary Clinton's out there like she's on the duck blind every Sunday, [like] she's packin' a six-shooter! C'mon! She knows better." Watch more of Obama's remarks »

But this isn't the first time in the primary race that the New York senator has spoken about unloading some shotgun shells.

At her first campaign stop in Wisconsin on February 16, Clinton told an audience at The Brat Stop in Kenosha about her childhood hunting experience.

"You know you may not believe it, but I've actually gone hunting," she said during a riff about gun control and protecting the Second Amendment. "I know, you may not believe it, but it's true. My father taught me to shoot a hundred years ago."

Mayors Against Illegal Guns, a group co-chaired by New York City Mayor Michael Bloomberg, plans to spend more than $1 million to air a television ad beginning this week urging Congress to close a loophole by forcing buyers at gun shows to undergo a federal background check.

The ad, which will air in Pennsylvania, New York, Arizona, Maryland and Florida, features clips from all three major presidential candidates.

"I'll be on your side for closing the gun show loophole," Clinton says. "Crack down on them. Close the gun show loopholes," Obama says.

And McCain adds, "Convicted criminals have been able to buy and sell thousands of guns at gun shows because of a loophole in the law. Close the loophole."

The issue has been a minefield for Democrats running for president.

Back in 2000, former Vice President Al Gore pushed for tougher gun laws and lost.

"The perception was that Al Gore's troubles in small towns and rural communities was based on the perception he was going to be tougher on gun laws than any other candidate," said Amy Walter, editor of National Journal's "The Hotline."

And now in 2008, both Democrats are careful to voice support for the Second Amendment.

"There is not a contradiction between protecting the Second Amendment rights of Americans and figuring out how we can keep, for example, assault weapons off the street," Clinton said on Saturday.

Clinton has been a supporter of gun control during her time in office. She voted for a 10-year extension of the assault weapons ban and voted for requiring extensive background checks at gun shows.

She also supports licensing and registration of handguns, mandatory trigger locks for handguns, holding adults responsible for their children's use of guns, raising the youth handgun ban from age 18 to 21, limiting gun sales to one per month and allowing the Consumer Products Safety Commission regulate guns. Read more about the candidates' positions on guns

Obama, meanwhile, supports extending the assault weapons ban; supports a national law against carrying concealed weapons, with exceptions for retired police and military personnel; and supports limiting gun sales to one per month.

But promises by all the candidates to protect the fundamental right to gun ownership won't impress the gun lobby.